1. Understanding Economic Indicators Scottish GDP as a case study in Indexation and Time Series Methods

2. What is GDP “Size” of economic output Overall Value (Annual) –Blue book, IO tables Short Term Trend Indicators –More frequent (quarterly) –(ONS do three estimates that successively incorporate three types of data.)

3. GVA concept Turning grapes into wine generates GVA Opening the bottle for you in a nice environment generates GVA Burning coal and transmitting power along lines generates GVA It’s a measure of “economic activity” GDP is the sum of all the GVA in the economy

4. Main Techniques 1 Sample Surveys –Mainly collected in cash values at current prices –Aggregated using standard techniques Ratio estimation Deflation –To convert current price to volume (constant price)

5. Main Techniques 2 Index numbers –To generate series that are comparable between different industries – there are no “units” –To weight together disparate measures to provide a whole economy picture Time Series methods –To allow publication of comparable quarterly figures for industries that are not comparable quarter by quarter

7. Simple Volume Indexation Imagine the price of your favourite commodity.

8. 100.00 =100x(£2.41/£2.41)£2.412000 134.4 =100x(£3.24/£2.41)£3.242009 129.9 =100x(£3.13/£2.41)£3.132008 124.5 =100x(£3.00/£2.41)£3.002007 119.5 =100x(£2.88/£2.41)£2.882006 115.8 =100x(£2.79/£2.41)£2.792005 112.0 =100x(£2.70/£2.41)£2.702004 108.7 =100x(£2.62/£2.41)£2.622003 105.8 =100x(£2.55/£2.41)£2.552002 102.9 =100x(£2.48/£2.41)£2.482001 IndexFormulaPriceYear

9. Man cannot live on beer alone

10. Obvious Strategy Is to track the rate of change of a weighted sum of the quantities of interest. E.g. price of an evenings entertainment: 2 x+ 1 x + 2/77 x But what about appropriate weights?

11. General price indices use a “basket” of goods “Currently, around 120,000 separate price quotations are used every month in compiling the indices, covering some 650 representative consumer goods and services” ONS CPI Note http://www.statistics.gov.uk/articles/nojournal/CPI-Basket-of-Goods-2009.pdf

13. Price vs Volume A volume index: –Aims to track change in quantities –Market price is an often used weight A price index: –Aims to track price i.e. inflation –Typically based on a basket of “output”

14. Base Weighted Volume Index Index of weighted volume Weights come from base year Also known as Laspeyres

15. Current Weighted Volume Index Index of volume Weights come from current year Also known as Paasche

16. Examples of Volume Index Calculations Year price (£) Number purchased per annum Amount spend on CDsMP3sCDsMP3sCDsMP3s 20041289310824 2005136697854 20061454 5670 Exercise: Calculate Base and Current Weighted Volume Indices for these data.

17. Comparison Number purchased per annum Laspeyres volume index Paasche volume index CDsMP3s 93 100.0 69 109.197.8 414 121.289.4

18. Economics People buy more things that get cheaper –And less things that get more expensive Known as the “Substitution effect” Laysperes index ignores this –Artificially high weight to fast growing/falling price commodities Paasche over weights its influence –Artificially low weight to fast growing/falling priced commodities

19. More Economics Laysperes generally considered an upper bound for growth Paasche generally considered a lower bound for growth “True Growth” is somewhere in between

20. Geometric Mean = 

21. Fisher “ideal” index

22. Comparison Number purchased per annum Laspeyres Volume index Paasche Volume index Fisher Volume Index CDsMP3s 9 3 100.0 6 9 109.197.8103.3 4 14 121.289.4104.1

23. Chainlinking Fisher is indeed an “ideal” measure But to compute it, you need price and volume data with the same resolution you want to publish In practice we use “chainlinking” on Laspeyres type indices

24. Chainlinking is Beyond the scope of this seminar

25. But it looks a bit like this.

26. Price Index Calculations Handout. YearBPICTPI 2000100.0 2001102.9103.2 2002105.8104.7 2003108.798.9 2004112.092.6 2005115.090.8 2006119.590.8 2007124.589.3 2008139.990.4 2009134.489.9

27. Answers Beer 2000 – 2004: 12.0% Cheese Toasty 2000-2004: -7.4% Beer 2004-2009: Cheese Toasty 04-09: Average Rate: Well, i.e. 3.9%

28. Time Series Analysis

29. Typical input series

30. Smoothing and Moving Averages Some data sources are highly volatile and/or seasonal; We may not be interested in these short- term fluctuations; Smoothing reduces these fluctuations and makes it easier to identify long-term trends;

31. A Store Retail Series - 500 1,000 1,500 2,000 2,500 3,000 3,500 4,000 2002Q12002Q22002Q32002Q42003Q12003Q22003Q32003Q42004Q12004Q22004Q32004Q4

32. MA t =average(x t-0.5,x t-1.5,x t+0.5,x t+1.5 ) A Store Retail Series - 500 1,000 1,500 2,000 2,500 3,000 3,500 4,000 2002Q12002Q22002Q32002Q42003Q12003Q22003Q32003Q42004Q12004Q22004Q32004Q4 Raw Data4-Point Moving Average

33. MA t =(x t-2 + 2*(x t-1 + x t + x t+1 ) + x t+2 )/8

34. MA t =(2*x t + 2*x t-1 + x t-2 )/5 A Store Retail Series - 500 1,000 1,500 2,000 2,500 3,000 3,500 4,000 2002Q12002Q22002Q32002Q42003Q12003Q22003Q32003Q42004Q12004Q22004Q32004Q4 Raw Data2 by 4 Moving Average

35. A Store Retail Series - 500 1,000 1,500 2,000 2,500 3,000 3,500 4,000 2002Q12002Q22002Q32002Q42003Q12003Q22003Q32003Q42004Q12004Q22004Q32004Q42005Q12005Q22005Q32005Q4 Raw Data2 by 4 Moving Average

36. Revisions

37. Exponential Smoothing Applies exponentially decreasing weights to observations as they get older; Alpha is essentially the proportion of the most recent data point that is allowed through; Fresh data doesn’t cause revisions; Movements are lagged compared with moving averages.

38. Comparison of MA with Exponential Smoothing for Volatile Soure Data 0 50 100 150 200 250 300 1234123412341234123412341234123412341234123412341234123412 199519961997199819992000200120022003200420052006200720082009 Source Data2*4 MAExponentially Smoothed

39. Choice of Alpha Alpha can be between 0 and 1; Generally this is a judgement call; but if it looks like we need a small alpha (below 0.7) then… Optimal value is one that minimises the Mean Squared Error: –i.e. the sum of

40. Summary Moving Average –Approximates the trend line; –Can remove seasonality; –Has difficulty at end points; –Prone to revisions. Exponential Smoothing –Lags movements in the data; –No Revisions.

41. Decomposing a time series A time series can be decomposed into: –The trend cycle component (medium and long term growth and cycles in the series) –The seasonal component (effects that are largely stable in timing, size and direction from year to year) –The irregular component (made up of anything remaining e.g. short term fluctuations, sampling and non-sampling errors, unpredictable effects due to one-off events such as strikes or disasters

42. Additive and Multiplicative series Additive series – seasonal effects are constant Multiplicative series – seasonal effects grow as series grows (and vice versa) 0 50 100 150 200 250 300 350 400 123412341234123412341234123412341234 200020012002200320042005200620072008 0 50 100 150 200 250 300 350 400 450 123412341234123412341234123412341234 200020012002200320042005200620072008

43. Time Series Models The additive model is: Time Series = Trend Cycle + Seasonal Component + Irregular Component Y = C + S + I The multiplicative model is: Time Series = Trend Cycle x Seasonal Component x Irregular Component Y = C x S x I

44. X-12-ARIMA Developed by the US Census Bureau. Estimating and removing regular seasonal patterns from time series data. This leaves the long term trend and short term irregular movements Worked example – Mains Gas supply (a component series of GDP) which is an additive series.

45. Question What was the quarterly change in Mains Gas Supply in the second quarter of 2009? In 2009Q1 the index was 121 and in 2009Q2 it was 79 giving a 35 per cent decrease. Is this a sensible answer?

46. Outlier Original Series = Trend-cycle + Seasonal Component + Irregular Component

47. Automatically identified as an ‘unusual’ value and effect scaled

48. Prior Adjusted Series – Initial Estimate of trend = Seasonal + Irregular Component

49. Decomposing Seasonal-Irregular Components into individual quarters…

51. Combining Seasonal Components for the individual quarters…

52. ‘Outliers’ put back in 8923-=66 89 23 66

53. X-12-ARIMA actual process

55. Question What was the quarterly change in Energy Use in the second quarter of 2009? In 2009Q1 the index was 121 and in 2009Q2 it was 79 giving a 35 per cent decrease. In 2009Q1 the seasonally adjusted index was 89 and in 2009Q2 it was 95 giving a 7 per cent increase.

56. Level Shift A step change In GDP could be caused by companies opening/closing Seasonal Break A change in the seasonal pattern In GDP could be caused by administrative changes

57. Exercise Discuss the charts on the handouts indentifying outliers, level shifts and seasonal breaks. Index of sales of motor vehicles, motorcycles and parts Index of sales biscuits, preserved pastry & cakes

58. 1. Index of sales of motor vehicles, motorcycles and parts Seasonal break 1999Q1 Additive Outlier 2001 Q4 Level Shift 2008 Q3?

59. 2. Index of sales biscuits, preserved pastry & cakes Seasonal break 1998Q3 Seasonal break 2002Q3 Additive Outlier 1995Q2 Additive Outlier 2009Q1? 0 20 40 60 80 100 120 140 160 180 200 1234123412341234123412341234123412341234123412341234123412 199519961997199819992000200120022003200420052006200720082009

60. Revisions New data always gives you new information Which will tell you more about your modelling assumptions Revisions are good